Cyclic‐Schottky strata of Schottky space

Abstract

AbstractSchottky space , where is an integer, is a connected complex orbifold of dimension ; it provides a parametrization of the ‐conjugacy classes of Schottky groups of rank . The branch locus , consisting of those conjugacy classes of Schottky groups being a finite index proper normal subgroup of some Kleinian group, is known to be connected. If , then there is a Kleinian group containing as a normal subgroup of index some prime integer . The structural description, in terms of Klein–Maskit Combination Theorems, of such a group is completely determined by a triple , where are integers such that . For each such tuple , there is a corresponding cyclic‐Schottky stratum . It is known that is connected. In this paper, for , we study the connectivity of these .